Hitting a Target An archer normally hits the target with...

Hitting a Target An archer normally hits the target with probability of $0.6 .$ She hires a new coach for a series of special lessons. After the lessons she hits the target in five out of eight attempts. (a) Find the probability that she would have hit five or more out of the eight attempts before her lessons with the new coach. (b) Did the new coaching effective if the probability in part (a) is 0.05 or less.)

Hitting a Target An archer normally hits the target with probability of $0.6 .$ She hires a new coach for a series of special lessons. After the lessons she hits the target in five out of eight attempts.
(a) Find the probability that she would have hit five or more out of the eight attempts before her lessons with the new coach.
(b) Did the new coaching effective if the probability in part (a) is 0.05 or less.)

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Key Concepts

Binomial Distribution

A binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. It is used whenever there are two possible outcomes (success or failure) and is characterized by the number of trials and the probability of success in each trial.

Hypothesis Testing

Hypothesis testing is a statistical method used to decide whether there is enough evidence in a sample of data to infer that a certain condition holds for the entire population. It involves comparing an observed outcome to what would be expected under a null hypothesis, which assumes no effect or no difference.

P-value

A p-value measures the probability of obtaining an outcome at least as extreme as the observed outcome under the assumption that the null hypothesis is true. It serves as a tool for decision-making in hypothesis testing, where a small p-value indicates that the observed data is unlikely under the null hypothesis.

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